Question

If (1, 2), (3, 4) and (0, 6) are the three vertices of a parallelogram taken in that order then the fourth vertex is ___________

• A. (2, 4)
• B. (-2, 4)
• C. (4, 2)
• D. (-4, 2)

Answer 1

The correct option is B (-2, 4)

Diagonals of a parallelogram bisect each other. So the midpoint of opposite two vertices, will be same as the mid points of the other two opposite vertices
Let fourth vertex be $(x,y)$
Midpoint of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
So midpoint of the diagonal 1 $=$ Midpoint of diagonal 2
$(\frac{1+0}{2},\frac{2+6}{2})=(\frac{3+x}{2},\frac{4+y}{2})$
Equating both the co-ordinates, we get
$3+x=1=>x=-2$
And $4+y=8=>y=4$
So, the fourth vertex is $(-2,4)$